Please help, it shouldent take too much time

The length of the side x is approximately 11.2 units.

A triangle is a three-sided polygon that is formed by connecting three non-collinear points in a plane. The three sides of a triangle are line segments that connect the vertices (corner points) of the triangle. The angles formed by the intersection of the sides are called interior angles of the triangle.

There are different ways to classify triangles based on their sides and angles. Based on sides, a triangle can be:

Equilateral: all three sides are equal in length.

Isosceles: two sides are equal in length.

Scalene: all three sides are of different lengths.

Based on angles, a triangle can be:

Acute: all three angles are acute (less than 90 degrees).

Right: one angle is a right angle (exactly 90 degrees).

Obtuse: one angle is obtuse (greater than 90 degrees).

In a right triangle, the side opposite the 68-degree angle is the hypotenuse, and the side adjacent to the 68-degree angle is the adjacent side. Therefore, we can use the trigonometric function cosine to find the length of the hypotenuse.

cos(68°) = adjacent/hypotenuse

cos(68°) = x/hypotenuse (since the adjacent side has length x)

We can rearrange the equation to solve for the hypotenuse:

hypotenuse = x/cos(68°)

Using a calculator, we can evaluate the expression for cos(68°) and substitute the given value for x to find the length of the hypotenuse:

hypotenuse = x/cos(68°) ≈ 36.9/x

Therefore, the length of the hypotenuse is approximately 36.9/x. We also know that the length of the other leg is 12. Using the Pythagorean theorem, we can find x:

x² + 12² = (36.9/x)²

Expanding the right side and simplifying, we get:

x⁴ - 15,129.6 = 0

Solving for x using a calculator, we get:

x ≈ 11.2 or x ≈ -11.2

Since x represents a length, it must be positive, so we take the positive value rounded to the nearest tenth:

x ≈ 11.2

Therefore, the length of the side x is approximately 11.2 units.

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The answer of the given question based on the proportional relationship the answer is he constant of proportionality is 45.

The constant of proportionality, also known as proportionality constant or unit rate, is  value that relates two quantities that are directly proportional to each other. In other words, if one quantity is multiplied by  constant of proportionality, other quantity will also be multiplied by same value.

We can find the constant of proportionality by calculating the ratio of the change in the number of replanted trees to the change in the area in acres.

From the given points, we can see that when the area is increased from 3 acres to 5 acres, the number of replanted trees is increased from 135 to 225. Therefore, the change in the number of trees is:

225 - 135 = 90

And the change in the area is:

5 - 3 = 2

So, the constant of proportionality is:

90/2 = 45

Therefore, the constant of proportionality is 45.

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The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides (legs) is equal to the square of the hypotenuse.

Mathematically, this is expressed as: a2 + b2 = c2, where a and b are the lengths of the two sides and c is the length of the hypotenuse. To calculate the hypotenuse of a right triangle, the Pythagorean Theorem can be used. Let's say the two sides of the triangle measure 3 and 4. To calculate the hypotenuse, use the formula c2 = a2 + b2, where c is the hypotenuse, a is 3, and b is 4. So, c2 = 32 + 42. This simplifies to c2 = 9 + 16, which equals c2 = 25. The square root of 25 is 5, so the hypotenuse of the triangle with sides 3 and 4 is 5.

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Answer:

By the figure I can say the X = 90⁰ and

Y = 90⁰

Answer:

A gap year can be a great option for some students after completing high school. It can provide an opportunity for personal growth, learning new skills, and gaining life experience. Gap years can also be used to travel, volunteer, or work to save money for future education.

The benefits of taking a gap year may include gaining independence, improving language skills, and gaining new perspectives on life. It can also provide an opportunity to explore different career options and interests before committing to a specific university program.

Some reasons for delaying a gap year may include financial considerations or the desire to start university right away. It's important to consider individual circumstances and goals when deciding whether to take a gap year or not.

The best way to spend a gap year will vary depending on individual interests and goals. Some options may include volunteering abroad, interning, working, or taking courses to improve skills or knowledge. It's important to research and plan ahead to make the most of the gap year experience.

Step-by-step explanation:

The decision to take a gap year after high school should be based on individual circumstances, goals, and interests.

It may be helpful for Zanele to consider her own priorities and plans for the future, and explore the various options available to her before making a decision.

A gap year can be a great option for some students after completing high school.

It allows them to take a break from formal education and explore other interests, gain work experience, or travel.

We have,

A gap year can be a great option for some students after completing high school.

It allows them to take a break from formal education and explore other interests, gain work experience, or travel.

It can also give them time to reflect on their goals and interests, and make a more informed decision about what they want to study in university or college.

Some benefits of taking a gap year include personal growth and development, gaining new skills and experiences, building independence and self-confidence, and developing a clearer sense of direction for future education and career goals.

There may be various reasons for delaying a gap year, such as financial constraints, a desire to enter the workforce or pursue other opportunities immediately, or a clear sense of direction and readiness for further education.

The best way to spend a gap year depends on individual interests, goals, and resources. Some common options include volunteering, interning, traveling, working, pursuing personal interests, or a combination of these activities. It is important to have a plan and goals for the gap year and to use the time productively and meaningfully.

Therefore,

The decision to take a gap year after high school should be based on individual circumstances, goals, and interests.

It may be helpful for Zanele to consider her own priorities and plans for the future, and explore the various options available to her before making a decision.

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Answer:

25% =1+(25/100)=1,25

15% = 1+(15/100)=1,15

increase coefficient 1,25*1,15=1,4375

percentage did the total number of students on the honor roll increase :

(1,4375-1)*100=43,75%

Step-by-step explanation:

To determine the price that the manufacturer should charge for each item to have a weekly revenue of $1,500, we first need to understand the relationship between the number of items sold, the price per item, and the revenue.

The revenue, R, can be calculated as the product of the number of items sold, x, and the price per item, p. Therefore, we can express the revenue as:

R = xp

In this case, we want to have a weekly revenue of $1,500, so we can set R equal to 1500 and solve for p:

1500 = x × p

Substituting the expression for x in terms of p given by the equation x = 800 - 100p, we get:

1500 = (800 - 100p) × p

Expanding and simplifying this equation, we get:

1500 = 800p - 100p²

or

100p² - 800p + 1500 = 0

We can solve for p using the quadratic formula:

[tex]p = \frac{(-b \pm \sqrt{(b^2 - 4ac)})}{2a}[/tex]

where a, b, and c are the coefficients of the quadratic equation.

In this case, we have:

a = 100

b = -800

c = 1500

Substituting these values into the quadratic formula, we get:

[tex]p = \frac{-(-800) \pm \sqrt{(-800)^2 - 4(100)(1500)}}{2 \times (100)}[/tex]

Simplifying this expression, we get:

[tex]p = \frac{800 \pm \sqrt{(160000 - 600000)}}{200}[/tex]

[tex]p = \frac{800 \pm \sqrt{(-440000)}}{200}[/tex]

Since the value inside the square root is negative, there are no real solutions for p. This means that the manufacturer cannot set a price per item that will result in a weekly revenue of $1,500 with the given equation.

However, we can use this equation to find the maximum revenue that the manufacturer can achieve by finding the vertex of the parabola represented by the quadratic equation. The x-coordinate of the vertex corresponds to the price per item that will result in the maximum revenue.

The x-coordinate of the vertex can be found using the formula:

x = -b / 2a

In this case, we have:

a = 100

b = -800

Substituting these values into the formula, we get:

x = -(-800) / 2(100)

  = 4

Therefore, the maximum revenue that the manufacturer can achieve is:

R = x × p  

  = 4 × (800 - 100(4))

  = $2400

To summarize, the manufacturer cannot set a price per item that will result in a weekly revenue of $1,500 with the given equation. However, using the equation, we can find the price per item that will result in the maximum revenue, which is $4. At this price, the manufacturer can achieve a weekly revenue of $2,400.

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Step-by-step explanation:

5/1 and 3/2

5/1 + 3/2 = 10/2 + 3/2 = 13/2 = 6 1/2

so, the sum is greater than 6.

5/1 - 3/2 = 10/2 - 3/2 = 7/2 = 3 1/2

so, the difference is less than 5.

a. Expressiοn is a prοduct οf twο binοmials

b. The factοrs οf the expressiοn (x+3)(9) are (x+3) and 9

c. The expressiοn (x+3)(9) represents the area οf the parallelοgram.

A parallelοgram is a fοur-sided plane figure with twο pairs οf parallel sides. It has οppοsite sides that are equal in length and οppοsite angles that are equal in measure. The area οf a parallelοgram is equal tο the prοduct οf its base and height.

a. Dariο's expressiοn is a prοduct οf twο binοmials: (x+3) and 9.

b. The factοrs οf the expressiοn (x+3)(9) are (x+3) and 9. The factοr (x+3) represents the length οf οne οf the sides οf the parallelοgram, while the factοr 9 represents the height οr perpendicular distance between the parallel sides οf the parallelοgram.

c. The expressiοn (x+3)(9) represents the area οf the parallelοgram. This is because the area οf a parallelοgram is equal tο the prοduct οf its base and height, and in this case, the base οf the parallelοgram is represented by the binοmial (x+3) and the height is represented by 9. Therefοre, the expressiοn (x+3)(9) is the area οf the parallelοgram with base (x+3) and height 9.

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Therefοre in 1.75 minutes, yοur friend cοuld clap his hands abοut 245 times.

When yοu "multiply" οr "times," yοu add the number tο itself several times. Fοr instance, multiplying 4 by 3 equals declaring that 4 + 4 + 4 = 12. As a result, multiplying the same number mοre than οnce prοduces faster results, such as 3 4 = 12.

We must first determine the number οf claps per secοnd that yοur friend cοuld make:

28 claps / 12 secοnds = 2.33 claps per secοnd

The number οf claps yοur friend cοuld make in 1.75 minutes can thus be calculated using this rate:

1 minute = 60 secοnds, sο 1.75 minutes = 1.75 x 60 = 105 secοnds

If yοur friend claps at a rate οf 2.33 claps every secοnd, in 105 secοnds they can:

2.33 claps per secοnd x 105 secοnds = 244.65 claps

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The expression used to find the total amount that the trader will get is 90x + 120y + N

To determine the total revenue, find the cost of 'x' pencils, and y pens. Now add the cost of three items and form an expression that  we can use to calculate the total amount got by the trader:

Here we have

A trader sells x pencils at 90 each,

y pens at 120 each and 5 erasers at N each  

Hence,

Cost of 'x' pencils = 90 × x = 90x

Cost of y pens = 120 × y = 120y

Cost of 5 erasers = 5N

Thus, the total amount that the trader will get = 90x + 120y + N

Therefore,

The expression that is used to find the total amount that the trader will get is 90x + 120y + N

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Answer:

Step-by-step explanation:

5x + 10 = 35

5x = 35 -10

5x = 25

x = 25/5

x = 5

Verification :

LHS = 5x + 10

RHS = 35

5(5) + 10 = 35

25 + 10 = 35

LHS = RHS

Hence verified!

Answer:

x = 5

Step-by-step explanation:

5x + 10 = 35

5x + 10 - 10 = 35 - 10

5x = 25

5x ÷ 5

25 ÷ 5

x = 5

Therefore, using the multiplier formula, a $525,000,000 increase in RGDP would result in a total increase in spending of $2,625,000,000.

To use the multiplier formula, we need to know the marginal propensity to consume (MPC), which is the fraction of each additional dollar of income that is spent on consumption.

The multiplier formula is: Multiplier = 1 / (1 - MPC)

If we assume an MPC of 0.8 (meaning that for every additional dollar of income, 80 cents are spent on consumption), the multiplier would be:

Multiplier = 1 / (1 - 0.8) = 5

So, if the change in Real Gross Domestic Product (RGDP) is $525,000,000, the total increase in spending (including consumption, investment, government spending, and net exports) would be:

Total spending increase = Multiplier x RGDP change

Total spending increase = 5 x $525,000,000

Total spending increase = $2,625,000,000

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Answer:

1. Liam's initial deposit was $2694.74 and Grace's initial deposit was $1894.74. 2. The system of equations that could be used to find their initial deposits is: I = g + 800, 0.009I = 0.011g

Step-by-step explanation:

Let's first use the formula for simple interest to find the interest earned by Liam and Grace after one year:

Interest earned by Liam = I x 0.009

Interest earned by Grace = g x 0.011

We also know that both Liam and Grace earn the same amount of interest after one year, so:

I x 0.009 = g x 0.011

We also know that Liam's initial deposit was $800 more than Grace's, so:

I = g + 800

Now we can substitute I in the first equation:

(g + 800) x 0.009 = g x 0.011

Simplifying and rearranging:

0.0072g + 7.2 = 0.011g

0.0038g = 7.2

g = 1894.74

Now we can find I:

I = g + 800

I = 1894.74 + 800

I = 2694.74

Therefore, Liam's initial deposit was $2694.74 and Grace's initial deposit was $1894.74.

The system of equations that could be used to find their initial deposits is:

I = g + 800

0.009I = 0.011g

Hope this helps! If you need more help, ask me! :]

Sorry if it's wrong.

Answer: Your welcome!

Step-by-step explanation:

a. An explicit formula for this sequence is an = 8 + 4(n - 1), where n is the number of the row in the sequence.

b. To determine the number of tiles in the 13th row, we substitute 13 for n in the explicit formula:

an = 8 + 4(13 - 1)

an = 8 + 48

an = 56

Therefore, the 13th row of the mosaic has 56 tiles.

Thanks! :) #BO

Answer:

a. an=4n + 4

b. 56 tiles

Step-by-step explanation:

a. We know that the first term of the arithmetic sequence is 8 and the second term is 12. Let's call the common difference between consecutive terms "d". Then we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, and d is the common difference.

Using this formula, we can find the explicit formula for the sequence:

a1 = 8

a2 = 12

d = a2 - a1 = 12 - 8 = 4

Therefore, the explicit formula for the sequence is:

an = 8 + 4(n - 1) = 4n + 4

b. We need to find the number of tiles in the 13th row, which means we need to find a13. Using the explicit formula we just found:

a13 = 4(13) + 4 = 56

Therefore, there are 56 tiles in the 13th row of the mosaic.

The 'b-a' part of the expression could be one of those elements.

Clair described the whole expression '2.b - a + 7'  as a sum of two elements.

So the given expression is 2.b - a + 7 ....(1)

Here, 2.b can be written as b + b

That is, 2.b = b+b .........(2)

Now substitute equation (2) in equation (1),

⇒ b + b - a + 7

By rearranging we get,

(b-a)+(b+7)

So, the expression 2.b - a + 7 is the sum of (b-a) and (b+7).

Therefore, Clair described the whole expression '2.b - a + 7'  as the sum of (b-a) and (b+7).

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Answer:

1/2 (one over two)

Step-by-step explanation:

when you are finding an a slope, or inequality as you wrote here, you are using formula: y/x ( y over x )

the graph dotes show how they are moving 2 to the right(x) and 1 up(y), so it’s 1/2!

Answer:

2/10

Step-by-step explanation:

Answer:

y-1>2

y<2-1 (group like terms, and change the sign)

y<1

The two unbiased estimators and their corresponding parameters are µ is an unbiased estimator for x. and p cap is and unbiased estimator of p.

Consider a sample of n observations (x1, x2,..., xn) that were selected from a population with an unknown mean. An impartial estimator for the population mean is the sample mean, indicated by the symbol u. Hence, E(u) = x.

Let's imagine we have a binary random variable that can only take on values of 0 or 1, with a success chance of p. We select n independent observations at random from this variable, and we define X as the sample's success rate. A fair estimate of the population percentage is the sample proportion, p cap = X/n. Hence, E(p cap) = p.

Hence, The two unbiased estimators and their corresponding parameters are µ is an unbiased estimator for x. and p cap is and unbiased estimator of p.

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Brandon's monthly "take-home salary" is $[tex]5,000[/tex] as a result as split his yearly take-home pay of $[tex]60,000[/tex] by 12 months.

Finding the value or quantity of a single unit of a given value or quantity and utilizing that information to find the value or quantity of the required number of units is known as the unitary method .The unitary technique, in other words, entails determining the value of one unit of a given quantity or value and then utilising that value to determine the value of any number of units. If an apple costs $2, for instance, you may use the unitary technique to calculate the price of five apples by multiplying the price of one apple by five.

Given,

To determine Brandon's monthly take-home pay, split his yearly take-home pay of $[tex]60,000[/tex] by [tex]12[/tex] months:

$[tex]60,000[/tex] ÷ [tex]12[/tex] = $[tex]5,000[/tex]

Brandon's monthly "take-home salary" is $[tex]5,000[/tex] as a result as split his yearly take-home pay of $[tex]60,000[/tex] by [tex]12[/tex] months.

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Both the volume of soft drinks in cans and the diameter of bolts immediately after manufacture is likely to follow a normal distribution.

What is the normal distribution?

A normal distribution is a type of continuous probability distribution in which most data points cluster toward the middle of the range, while the rest taper off symmetrically toward either extreme. The middle of the range is also known as the mean of the distribution.

a) The volume of soft drinks in cans is likely to follow a normal distribution because it is produced using a standardized manufacturing process.

This process is designed to ensure that each can has the same volume of liquid, within a certain tolerance level.

The manufacturing process typically involves using machines to fill and seal the cans, which reduces the likelihood of any significant variation in volume.

Additionally, the volume of soft drinks in cans can be expected to follow a normal distribution due to the central limit theorem, which states that the distribution of sample means from a population with any distribution tends to be normal as the sample size increases.

b) The diameter of bolts immediately after manufacture is likely to follow a normal distribution because it is a measurement that can be precisely controlled during the manufacturing process.

The process typically involves using machines that are calibrated to produce bolts with a specific diameter.

Any variation in diameter that occurs is likely to be small and random, due to factors such as machine error or natural variation in the raw materials used to produce the bolts.

Additionally, the diameter of bolts can be expected to follow a normal distribution due to the central limit theorem, which states that the distribution of sample means from a population with any distribution tends to be normal as the sample size increases.

Hence, both the volume of soft drinks in cans and the diameter of bolts immediately after manufacture are likely to follow a normal distribution.

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Simplifying negative 3 and two-thirds minus 6 and three-fourths is negative 10 and five-twelfths. Option C

To subtract mixed numbers, we first need to convert them to improper fractions.

Negative 3 and two-thirds can be written as - (3 + 2/3) = - (9/3 + 2/3) = -11/3

Similarly, 6 and three-fourths can be written as 6 + 3/4 = (24/4) + 3/4 = 27/4

Now, we can subtract these fractions:

-11/3 - 27/4 = (-44/12) - (81/12) = -125/12

Finally, we can convert this improper fraction back to a mixed number:

-125/12 = -10 and 5/12

Therefore, the answer is negative 10 and five-twelfths.

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The tοtal prοductiοn fοr fοοd shοuld be $1,000,000.

The fοur basic mathematical οperatiοns are Additiοn, subtractiοn, multiplicatiοn, and divisiοn.

Let F and B be the prοductiοn οf fοοd and building, respectively, in dοllars. Then, we have the fοllοwing system οf equatiοns:

Fοr the prοductiοn οf fοοd:

F = 0.20F + 0.25B + 100,000

0.20F + 0.15B = 100,000

Fοr the prοductiοn οf building:

B = 0.20F + 0.25B + 200,000

0.25B + 0.20F = 200,000

We can sοlve this system using substitutiοn οr eliminatiοn. Here, we will use eliminatiοn:

0.20F + 0.25B = 200,000 (multiply the secοnd equatiοn by -1)

0.20F + 0.15B = 100,000

0.10B = 100,000 - 0.10F (subtract the secοnd equatiοn frοm the first)

B = 1,000,000 - F

Substitute this expressiοn fοr B intο οne οf the equatiοns tο sοlve fοr F:

0.20F + 0.25(1,000,000 - F) = 200,000

0.20F + 250,000 - 0.25F = 200,000

-0.05F = -50,000

F = 1,000,000

Hence, the tοtal prοductiοn fοr fοοd shοuld be $1,000,000.

We can substitute this value intο either equatiοn tο sοlve fοr B:

0.20(1,000,000) + 0.15B = 100,000

0.15B = -80,000

B = -533,333.33

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Step-by-step explanation:

339 = 13 s      divide both sides by 13

s = 26.08

Maybe you meant

39 = 13 s    divide both sides of the equation by 13

s = 3

Answer:

120, because YXS is 120, or XST is 120.

The area of the regular decagon is 325 square units

The formula for the area of a regular polygon is given by

Area (A) = [number of sides (n) * length of side (l) * apothem (a)] /2

Apothem Formula is given by:

For the decagon, n = 10 (10 sides) and a = 10

a = l / 2tan(180/n)°

10 = l / 2tan(180/10)°

10 = l / 2 tan18°

l = 10 * 2 * tan18°

l = 6.50 units

Finding Area:

A = [number of sides (n) * length of side (l) * apothem (a)] /2

A = (10 * 6.50 * 10)/2

A = 325 square units

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The coordinates of the points of intersection of the graph with coordinate axes are (2, 0) and (0, 3).

The equation of a line is given by y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, m = -1.5 and b = 3. To find the x-intercept, we need to solve for x when y = 0. When y = 0, 0 = -1.5x + 3. Solving for x, we get x = 2. To find the y-intercept, we need to solve for y when x = 0. When x = 0, 0 = -1.5(0) + 3. Solving for y, we get y = 3. Therefore, the coordinates of the points of intersection of the graph with coordinate axes are (2, 0) and (0, 3).

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Answer: The last option. X is greater than or equal to -3

Step-by-step explanation:

If you are searching for all of the values highlighted in red, then it must be every single value greater than x=-3 including the value itself (the dot located on the value is shaded, therefore you must include it within the domain).